You can co- wash as often as you want. Some people do wet or cleanse daily, others less often. Depending on your hair, co-washing might not be the answer, so keep in mind that there are lots of other options that are still curl (and CG) friendly, such as cleansing conditioners and sulfate-free shampoos (low-poos).
As far as silicones, some do end in -cone, but they can also end in -xane, or -conol. Some silicones are water soluble and therefore CG friendly. These usually have PEG or PPG in front of the name. There are exceptions to the name thing, but there are ton of good articles by Curl Chemist that can explain more of the ins an outs. And sulfates are not necessary to remove silicones. Any cleanser with coco betaine will do the trick, so don't feel like you have to stop using something you love just because it has silicones.